3 problems

Let $\lambda\in X^+$ satisfy $\overline{\lambda}=\overline{0}$, and let $w_0\in V(\lambda)$ be the vector, unique up to nonzero scalar multiple, whose $\mathbf{U}^\imath$-submodule…

Let $\mathbf{U}^\imath$ be the imathquantum group with parameters ${\boldsymbol \varsigma}$ and ${\boldsymbol \kappa}$. For each $\lambda,\mu,\nu\in X^+$, let…

Braid group automorphism conjecture. For every such $i$, there exist mutually inverse algebra automorphisms $\mathbf T_{i,e}'$ and $\mathbf T_{i,-e}”$ of…